Search results for: altering function

Authors: D. S. Palimkar

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Random fixed point theory has received much attention in recent years, and it is needed for the study of various classes of random equations. The study of random fixed point theorems was initiated by the Prague school of probabilistic in the 1950s. The existence and uniqueness of fixed points for the self-maps of a metric space by altering distances between the points with the use of a control function is an interesting aspect in the classical fixed point theory. In a new category of fixed point problems for a single self-map with the help of a control function that alters the distance between two points in a metric space which they called an altering distance function. In this paper, we prove the results of existence of random common fixed point and its uniqueness for a pair of random mappings under weakly contractive condition for generalizing alter distance function in polish spaces using Random Common Fixed Point Theorem for Generalized Weakly Contractions.

Keywords: Polish space, random common fixed point theorem, weakly contractive mapping, altering function

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Authors: Jia-Ming Kok, Javaan Chahl

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An optimisation method using both global and local optimisation is implemented to determine the flapping profile which will produce the most lift for an experimental wing-actuation system. The optimisation method is tested using a numerical quasi-steady analysis. Results of an optimised flapping profile show a 20% increase in lift generated as compared to flapping profiles obtained by high speed cinematography of a Sympetrum frequens dragonfly. Initial optimisation procedures showed 3166 objective function evaluations. The global optimisation parameters - initial sample size and stage one sample size, were altered to reduce the number of function evaluations. Altering the stage one sample size had no significant effect. It was found that reducing the initial sample size to 400 would allow a reduction in computational effort to approximately 1500 function evaluations without compromising the global solvers ability to locate potential minima. To further reduce the optimisation effort required, we increase the local solver’s convergence tolerance criterion. An increase in the tolerance from 0.02N to 0.05N decreased the number of function evaluations by another 20%. However, this potentially reduces the maximum obtainable lift by up to 0.025N.

Keywords: flapping wing, optimisation, quasi-steady model, dragonfly

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb

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The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.

Keywords: DCF, PCF, throughput, NS2

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Authors: Shatha S. Alhily

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The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.

Keywords: derivative, integral means, self conformal maps, univalent function

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang

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A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.

Keywords: beta function, compressor map, interpolation error, map optimization tool

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Authors: Filip Stojcevski, Tim Hilditch, Luke Henderson

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Although carbon fibre composites are becoming ever more prominent in the engineering industry, interfacial failure still remains one of the most common limitations to material performance. Carbon fiber surface treatments have played a major role in advancing composite properties however research into the influence of manufacturing variables on a fiber manufacturing line is lacking. This project investigates the impact of altering carbon fiber manufacturing conditions on a production line (specifically electrochemical oxidization and sizing variables) to assess fiber-matrix adhesion. Pristine virgin fibers were manufactured and interfacial adhesion systematically assessed from a microscale (single fiber) to a mesoscale (12k tow), and ultimately a macroscale (laminate). Correlations between interfacial shear strength (IFSS) at each level is explored as a function of known interfacial bonding mechanisms; namely mechanical interlocking, chemical adhesion and fiber wetting. Impact of these bonding mechanisms is assessed through extensive mechanical, topological and chemical characterisation. They are correlated to performance as a function of IFSS. Ultimately this study provides a bottoms up approach to improving composite laminates. By understanding the scaling effects from a singular fiber to a composite laminate and linking this knowledge to specific bonding mechanisms, material scientists can make an informed decision on the manufacturing conditions most beneficial for interfacial adhesion.

Keywords: carbon fibers, interfacial adhesion, surface treatment, sizing

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Authors: Xia Huo

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Children are more vulnerable to environmental toxicants compared to adults, and their developing immune system is among the most sensitive targets regarding toxicity of environmental toxicants. Studies have found that exposure to environmental toxicants is associated with impaired immune function in children, but only a few studies have focused on the relationship between environmental toxicant exposure and vaccine antibody potency and immunoglobulin (Ig) levels in children. These studies investigated the associations of exposure to polychlorinated biphenyls (PCBs), perfluorinated compounds (PFCs), heavy metals (Pb, Cd, As, Hg) and PM2.5 with the serum-specific antibody concentrations and Ig levels against different vaccines, such as anti-Hib, tetanus, diphtheria toxoid, and analyze the possible mechanisms underlying exposure-related alterations of antibody titers and Ig levels against different vaccines. Results suggest that exposure to these toxicants is generally associated with decreased potency of antibodies produced from childhood immunizations and an overall deficiency in the protection the vaccines provide. Toxicant exposure is associated with vaccination failure and decreased antibody titers, and increased risk of immune-related diseases in children by altering specific immunoglobulin levels. Age, sex, nutritional status, and co-exposure may influence the effects of toxicants on the immune function in children. Epidemiological evidence suggests that exposure-induced changes to humoral immunerelated tissue/cells/molecules response to vaccines may have predominant roles in the inverse associations between antibody responsiveness to vaccines and environmental toxicants. These results help us to conduct better immunization policies for children under environmental toxicant burden.

Keywords: environmental toxicants, immunotoxicity, vaccination, antibodies, children's health

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Authors: Lalnuntluanga Hmar, Hardik Vyas

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Hydraulic fracturing has become an essential procedure to break apart the rock and release the oil or gas which are trapped tightly in the rock by pumping fracturing fluids at high pressure down into the well. To open the fracture and to transport propping agent along the fracture, proper selection of fracturing fluids is the most crucial components in fracturing operations. Rheology properties of the fluids are usually considered the most important. Among various fracturing fluids, Borate crosslinked fluids have proved to be highly effective. Borate in the form of Boric Acid, borate ion is the most commonly use to crosslink the hydrated polymers and to produce very viscous gels that can stable at high temperature. Guar and HPG (Hydroxypropyl Guar) polymers are the most often used in these fluids. Borate gel rheology is known to be a function of polymer concentration, borate ion concentration, pH, and temperature. The crosslinking using Borate is a function of pH which means it can be formed or reversed simply by altering the pH of the fluid system. The fluid system was prepared by mixing base polymer with water at pH ranging between 8 to 11 and the optimum borate crosslinker efficiency was found to be pH of about 10. The rheology of laboratory prepared Borate crosslinked fracturing fluid was determined using Anton Paar Rheometer and Fann Viscometer. The viscosity was measured at high temperature ranging from 200ᵒF to 250ᵒF and pressures in order to partially stimulate the downhole condition. Rheological measurements reported that the crosslinking increases the viscosity, elasticity and thus fluid capability to transport propping agent.

Keywords: borate, crosslinker, Guar, Hydroxypropyl Guar (HPG), rheology

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

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The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.

Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function

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Authors: A. Ibovi Mouondayi, S. Zaher, R. Assadi, K. Erraoui, S. Sboul, J. Daoudim, S. Bousselham, K. Nassar, S. Janani

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Introduction: Neuropathic pain (NP) is chronic pain; it can be observed in a large number of clinical situations. This pain results from a lesion of the peripheral or central nervous system. It is a frequent reason for consultations in rheumatology. This pain being chronic, can become disabling for the patient, thereby altering his quality of life. Objective: The objective of this study was to evaluate the impact of neuropathic pain on the quality of life of patients followed-up for chronic neuropathic pain. Material and Method: This is a monocentric, cross-sectional, descriptive, retrospective study conducted in our department over a period of 19 months from October 2020 to April 2022. The missing parameters were collected during phone calls of the patients concerned. The diagnostic tool adopted was the DN4 questionnaire in the dialectal Arabic version. The impact of NP was assessed by the visual analog scale (VAS) on pain, sleep, and function. The impact of PN on mood was assessed by the hospital anxiety, and depression scale (HAD) score in the validated Arabic version. The exclusion criteria were patients followed up for depression and other psychiatric pathologies. Results: A total of 1528 patient data were collected; the average age of the patients was 57 years (standard deviation: 13 years) with extremes ranging from 17 years to 94 years, 91% were women and 9% men with a sex ratio man/woman equal to 0.10. 67% of our patients were married, and 63% of our patients were housewives. 43% of patients were followed-up for degenerative pathology. The NP was cervical radiculopathy in 26%, lumbosacral radiculopathy in 51%, and carpal tunnel syndrome in 20%. 23% of our patients had poor sleep quality, and 54% had average sleep quality. The pain was very intense in 5% of patients; 33% had severe pain, and 58% had moderate pain. The function was limited in 55% of patients. The average HAD score for anxiety and depression was 4.39 (standard deviation: 2.77) and 3.21 (standard deviation: 2.89), respectively. Conclusion: Our data clearly illustrate that neuropathic pain has a negative impact on the quality of sleep and function, as well as the mood of patients, thus influencing their quality of life.

Keywords: neuropathic pain, sleep, quality of life, chronic pain

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Authors: Naga Velamakuri, Jyothi K. Reddy

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Quality must be designed into a product and not inspected has become the main motto of all the companies globally. Due to the rapidly increasing technology in the past few decades, the nature of demands from the consumers has become more sophisticated. To sustain this global revolution of innovation in production systems, companies have to take steps to accommodate this technology growth. In this process of understanding the customers' expectations, all the firms globally take steps to deliver a perfect output. Most of these techniques also concentrate on the consistent development and optimization of the product to exceed the expectations. Quality Function Deployment(QFD) and Modular Function Deployment(MFD) are such techniques which rely on the voice of the customer and help deliver the needs. In this paper, Quality Function Deployment and Modular Function Deployment techniques which help in converting the quantitative descriptions to qualitative outcomes are discussed. The area of interest would be to understand the scope of each of the techniques and the application range in product development when these are applied together to any problem. The research question would be mainly aimed at comprehending the limitations using modularity in product development.

Keywords: quality function deployment, modular function deployment, house of quality, methodology

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Authors: Krishnamoorthy Sathiyan, Shanti Gopal Patra, Ronen Bar-Ziv, Tomer Zidki

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Developing efficient non-noble metal catalysts that are cheap and durable for oxygen evolution reaction (OER) is a great challenge. Moreover, altering the electronic structure of the catalyst and structural engineering of the materials provide a new direction for enhancing the OER. Herein, we have successfully synthesized Fe and Co incorporated MoS₂ catalysts, which show improved catalytic activity for OER when compared with MoS₂, Fe-MoS₂, and Co-MoS₂. It was found that at an optimal ratio of Fe and Co, the electronic and structural modification of MoS₂ occurs, which leads to change in orientation and thereby enhances the active catalytic sites on the edges, which are more exposed for OER. The nanocomposites have been well characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), and energy dispersive X-ray analysis (EDX), Elemental Mapping, transmission electron microscope (TEM), and high-resolution transmission electron microscope (HR-TEM) analysis. Among all, a particular ratio of FeCo-MoS₂ exhibits a much smaller onset with better catalytic current density. The remarkable catalytic activity is mainly attributed to the synergistic effect from the Fe and Co. Most importantly, our work provides an essential insight in altering the electronic structure of MoS₂ based materials by incorporating promoters such as Co and Fe in an optimal amount, which enhances OER activity.

Keywords: electrocatalysts, molybdenum disulfide, oxygen evolution reaction, transition metals

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Authors: Myunggon Yoon, Jung-Ho Moon

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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: combustor, dynamics, thermoacoustics, transfer function

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Authors: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Aziza Barnawi

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Background: Regular exercise reduces risk factors associated with cardiovascular diseases. Over the past decade, exercise interventions have been introduced to reduce the risk of and prevent coronary artery disease (CAD). Elevated low-density lipoproteins (LDL) contribute to the formation of atherosclerosis, its manifestations on the endothelial narrow the coronary artery and affect the endothelial function. Therefore, flow-mediated dilation (FMD) technique is used to assess the function. The results of previous studies have been inconsistent and difficult to interpret across different types of exercise programs. The relationship between exercise therapy and lipid levels has been extensively studied, and it is known to improve the lipid profile and endothelial function. However, the effectiveness of exercise in altering LDL levels and improving blood flow is controversial. Objective: This review aims to explore the evidence and quantify the impact of exercise training on LDL levels and vascular function by FMD. Methods: Electronic databases were searched PubMed, Google Scholar, Web of Science, the Cochrane Library, and EBSCO using the keywords: “low and/or moderate aerobic training”, “blood flow”, “atherosclerosis”, “LDL mediated blood flow”, “Cardiac Rehabilitation”, “low-density lipoproteins”, “flow-mediated dilation”, “endothelial function”, “brachial artery flow-mediated dilation”, “oxidized low-density lipoproteins” and “coronary artery disease”. The studies were conducted for 6 weeks or more and influenced LDL levels and/or FMD. Studies with different intensity training and endurance training in healthy or CAD individuals were included. Results: Twenty-one randomized controlled trials (RCTs) (14 FMD and 7 LDL studies) with 776 participants (605 exercise participants and 171 control participants) met eligibility criteria and were included in the systematic review. Endurance training resulted in a greater reduction in LDL levels and their subfractions and a better FMD response. Overall, the training groups showed improved physical fitness status compared with the control groups. Participants whose exercise duration was ≥150 minutes /week had significant improvement in FMD and LDL levels compared with those with <150 minutes/week.Conclusion: In conclusion, although the relationship between physical training, LDL levels, and blood flow in CAD is complex and multifaceted, there are promising results for controlling primary and secondary prevention of CAD by exercise. Exercise training, including resistance, aerobic, and interval training, is positively correlated with improved FMD. However, the small body of evidence for LDL studies (resistance and interval training) did not prove to be significantly associated with improved blood flow. Increasing evidence suggests that exercise training is a promising adjunctive therapy to improve cardiovascular health, potentially improving blood flow and contributing to the overall management of CAD.

Keywords: exercise training, low density lipoprotein, flow mediated dilation, coronary artery disease

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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Authors: Lanyan Peng, Ling Chen

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Leishan Miao New-Year is one of the grandest festivals in the southeastern of Guizhou Province in China. It was officially listed in the National Intangible Cultural Heritage List in 2008, as a traditional folk cultural activity organized by the local Miao people. With the rise of cultural tourism, after 19 years of exploration, the local government has successfully built Miao New-Year into a cultural card that is well-known at home and abroad. During the Miao New-Year period, it has attracted 3.8 million tourists and achieves a win-win situation in the economy and culture. However, tourism development has changed the living environment and living state of the local people. And it is accompanied by changes in the form of the festival, the content of the festival, and the local people’s needs and attitudes to the festival. This paper uses the field investigation method to achieve 410 questionnaires and 35 interviews, exploring the process and the reasons for changes of Leishan Miao New-Year’s cultural function. Among all the functions, the economic function, identity function, and entertainment function have been enhanced, and the marriage and love function has been extended. In the meanwhile, sacrificial function has been weakened. There are some trends in functions. The function of commemorating ancestor and self-entertainment has been changed to entertaining people and economic pursuit.

Keywords: Miao New-Year, Miao nationality, festival function, changes

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Authors: Irina Peterburgsky

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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Bina Kumari, Subir K. Sarkar, Pradipta Bandyopadhyay

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The autocorrelation function of the density fluctuation is studied in each of the two phases in a Gibbs Ensemble Monte Carlo (GEMC) simulation of the problem of phase separation for a square well potential with various values of its range. We find that the normalized autocorrelation function is described very well as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of (α, τ₁, τ₂) on the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We also analyse the issue of how to choose the parameters of the GEMC simulation optimally.

Keywords: autocorrelation function, density fluctuation, GEMC, simulation

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Authors: Yuan Zheng

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3D model-based vehicle matching provides a new way for vehicle recognition, localization and tracking. Its key is to construct an evaluation function, also called fitness function, to measure the degree of vehicle matching. The existing fitness functions often poorly perform when the clutter and occlusion exist in traffic scenarios. In this paper, we present a practical and efficient fitness function. Unlike the existing evaluation functions, the proposed fitness function is to study the vehicle matching problem from both local and global perspectives, which exploits the pixel gradient information as well as the silhouette information. In view of the discrepancy between 3D vehicle model and real vehicle, a weighting strategy is introduced to differently treat the fitting of the model’s wireframes. Additionally, a normalization operation for the model’s projection is performed to improve the accuracy of the matching. Experimental results on real traffic videos reveal that the proposed fitness function is efficient and robust to the cluttered background and partial occlusion.

Keywords: 3D-2D matching, fitness function, 3D vehicle model, local image gradient, silhouette information

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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